A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the string and pulls the cylinder towards him (figure 10-Q4). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands isA. lB. 2lC. 3lD. 4l

The cylinder needs to reach the person i.e. To travel a total of distance L. Let us assume the radius to be r.

We know that the length of an arc is

Hence

So to cover the distance L it needs extra arc length of,

Hence it covers extra L length.

So, the total length will be ,2L.

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